# An LSPR-Based Kinetic Framework for Polyelectrolyte Molecular Weight Determination: A Proof-of-Concept Study

## TL;DR

This paper introduces a new method using LSPR to determine the molecular weight of polyelectrolytes without traditional techniques.

## Contribution

A novel, calibration-free LSPR-based kinetic framework for determining polyelectrolyte molecular weight is introduced.

## Key findings

- The molecular weight of PAZO was calculated as 257,400 g mol–1 using the LSPR method.
- LSPR-based kinetics offer a surface-sensitive alternative to traditional methods like SEC.
- The method assumes symmetry in association rate constants, supported by electrostatic interaction reciprocity.

## Abstract

Determining the molecular weight of polyelectrolytes
remains a
persistent challenge because conventional techniques such as size-exclusion
chromatography (SEC) often require added salt, calibration against
neutral polymers, and complex optimization to overcome chain–column
interactions. Here we introduce a kinetics-based method that employs
Localized Surface Plasmon Resonance (LSPR) to measure the real-time
electrostatic complexation of poly­(ethylenimine) (PEI) and poly­[1-[4-(3-carboxy-4-hydroxyphenylazo)­benzenesulfonamido]-1,2-ethanediyl,
sodium salt] (PAZO). By extracting association and dissociation rate
constants from concentration-dependent binding transients, we establish
a calibration-free approach to determining the number-average molecular
weight (M

n
) of polyelectrolytes
under dilute, salt-free conditions. Using the known M

n
of PEI, the M

n
of PAZO was calculated as 257,400 g mol–1, corresponding to a degree of polymerization of 642.
This analysis assumes symmetry of the association rate constant (k

on
) across binding orientations,
an assumption justified by the reciprocal nature of electrostatic
interactions. The results highlight LSPR-based kinetics as a powerful,
surface-sensitive alternative to traditional methods, offering a broadly
adaptable strategy for characterizing charged polymers and other biomolecular
systems. This study is presented as a proof-of-concept demonstration,
emphasizing the novelty and feasibility of the LSPR-based kinetic
framework rather than exhaustive validation of molecular weight determinations.
By focusing on methodological innovation, the work highlights a generalizable
strategy for polyelectrolyte characterization that can be extended
and refined in future investigations.